PCHGCN: Physically Constrained Higher-Order Graph Convolutional Network for Pedestrian Trajectory Prediction

Pedestrian trajectory prediction is crucial in fields, such as autonomous driving and robot navigation, but it remains challenging due to the complex social interactions among pedestrians. Previous trajectory prediction methods are limited by redundant interactions that make it difficult to accurately model higher-order social relations and capture the indirect effects of surrounding pedestrians. To address these challenges, we propose a physically constrained higher-order graph convolutional network (PCHGCN) for pedestrian trajectory prediction. PCHGCN first constructs a spatial graph and adopts the attention mechanism to obtain an attention score matrix representing the social interactions of pedestrians. Then, the higher-order social interactions are obtained through multiple matrix power operations of the higher-order graph module. To eliminate redundant interactions in higher-order social interactions, we design a physical constraint module to constrain the modeling of higher-order social interactions according to physical characteristics of distance, field of view, and distance transformation rate between pedestrians. Additionally, we design a gated fusion module that assigns weights to higher-order social interactions, ensuring the rational utilization of different degrees of social relations. Finally, we introduce the last frame velocity as physical prior knowledge to dynamically correct the predicted trajectory of the constant velocity model to improve the accuracy and diversity of future trajectory prediction. Experiments on ETH, UCY, and SDD datasets demonstrate that our method outperforms existing methods, achieving superior prediction performance with only 15.3K model parameters. The code is publicly available at https://github.com/Chenwangxing/PCHGCN-Master.